The Warriors are left bottom of Pool 4 with just one point to their name, their hopes of progressing to the quarter-finals over for another campaign.
But ahead of a return fixture in France Townsend doesn't want his RaboDirect PRO12 outfit throwing in the towel, insisting they simply were not good enough last time out.
"We must go to France and produce a performance that shows what wearing a Glasgow shirt is all about," Townsend told the Evening Times.
"The bottom line is Europe has now gone for another year but what is on the line is our pride.
"We know that Friday was unacceptable. We had the chance to provide a response to the defeat in Munster and we just did not take it, we let the Glasgow jersey and the support down badly.
"We know that we are out of the tournament and that is very disappointing, but at the same time we have to have to go out there and show what Glasgow Warriors are all about.
"Mistakes happen but the level we produced on Friday was simply not on. On top of that, Castres did not have to play well to win and that is very annoying."
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